Suppose that the flight of a launched bottle rocket can be modeled by the function [math]f(x) = –(x – 1)(x – 6)[/math], where [math]f(x)[/math] measures the height above the ground in meters and [math]x[/math] represents the horizontal distance in meters from the launching spot at [math]x = 1[/math]. How far does the bottle rocket travel in the horizontal direction from launch to landing? What is the maximum height the bottle rocket reaches? How far has the bottle rocket traveled horizontally when it reaches its maximum height? Graph the function.
[list=1] [*]Identify the [math]x[/math]-intercepts of the function. [*]Determine the maximum height of the bottle rocket. [*]Determine the horizontal distance from the launch point to the maximum height of the bottle rocket. [*]Graph the function. [/list]